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Register a new userWhy have asset price properties changed so little in 200 years
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We first review empirical evidence that asset prices have had episodes of large fluctuations and been inefficient for at least 200 years. We briefly review recent theoretical results as well as the neurological basis of trend following and finally argue that these asset price properties can be attributed to two fundamental mechanisms that have not changed for many centuries: an innate preference for trend following and the collective tendency to exploit as much as possible detectable price arbitrage, which leads to destabilizing feedback loops.
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Understanding the statistical properties of recurrence intervals of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have been extensively investigated. However, the impacts of microscopic rules of a complex system on the macroscopic properties of its recurrence intervals are less studied. In this Letter, we adopt an order-driven stock market model to address this issue for stock returns. We find that the distributions of the scaled recurrence intervals of simulated returns have a power law scaling with stretched exponential cutoff and the intervals possess multifractal nature, which are consistent with empirical results. We further investigate the effects of long memory in the directions (or signs) and relative prices of the order flow on the characteristic quantities of these properties. It is found that the long memory in the order directions (Hurst index $H_s$) has a negligible effect on the interval distributions and the multifractal nature. In contrast, the power-law exponent of the interval distribution increases linearly with respect to the Hurst index $H_x$ of the relative prices, and the singularity width of the multifractal nature fluctuates around a constant value when $H_x<0.7$ and then increases with $H_x$. No evident effects of $H_s$ and $H_x$ are found on the long memory of the recurrence intervals. Our results indicate that the nontrivial properties of the recurrence intervals of returns are mainly caused by traders behaviors of persistently placing new orders around the best bid and ask prices.
Twenty years ago Breiman (2001) called to our attention a significant cultural division in modeling and data analysis between the stochastic data models and the algorithmic models. Out of his deep concern that the statistical community was so deeply and almost exclusively committed to the former, Breiman warned that we were losing our abilities to solve many real-world problems. Breiman was not the first, and certainly not the only statistician, to sound the alarm; we may refer to none other than John Tukey who wrote almost 60 years ago data analysis is intrinsically an empirical science. However, the bluntness and timeliness of Breimans article made it uniquely influential. It prepared us for the data science era and encouraged a new generation of statisticians to embrace a more broadly defined discipline. Some might argue that The cultural division between these two statistical learning frameworks has been growing at a steady pace in recent years, to quote Mukhopadhyay and Wang (2020). In this commentary, we focus on some of the positive changes over the past 20 years and offer an optimistic outlook for our profession.
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem using singular perturbation methods. We prove, by constructing sub- and super-solutions, that the approximations are accurate to the specified order. Finally, we perform some numerical experiments to illustrate the effect that stochastic trading frictions have on optimal trading.
I revisit two theories of cell differentiation in multicellular organisms published a half-century ago, Stuart Kauffmans global gene regulatory dynamics (GGRD) model and Roy Brittens and Eric Davidsons modular gene regulatory network (MGRN) model, in light of newer knowledge of mechanisms of gene regulation in the metazoans (animals). The two models continue to inform hypotheses and computational studies of differentiation of lineage-adjacent cell types. However, their shared notion (based on bacterial regulatory systems) of gene switches and networks built from them, have constrained progress in understanding the dynamics and evolution of differentiation. Recent work has described unique write-read-rewrite chromatin-based expression encoding in eukaryotes, as well metazoan-specific processes of gene activation and silencing in condensed-phase, enhancer-recruiting regulatory hubs, employing disordered proteins, including transcription factors, with context-dependent identities. These findings suggest an evolutionary scenario in which the origination of differentiation in animals, rather than depending exclusively on adaptive natural selection, emerged as a consequence of a type of multicellularity in which the novel metazoan gene regulatory apparatus was readily mobilized to amplify and exaggerate inherent cell functions of unicellular ancestors. The plausibility of this hypothesis is illustrated by the evolution of the developmental role of Grainyhead-like in the formation of epithelium.
In this paper, we investigate the cooling-off effect (opposite to the magnet effect) from two aspects. Firstly, from the viewpoint of dynamics, we study the existence of the cooling-off effect by following the dynamical evolution of some financial variables over a period of time before the stock price hits its limit. Secondly, from the probability perspective, we investigate, with the logit model, the existence of the cooling-off effect through analyzing the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 and inspecting the trading period from the opening phase prior to the moment that the stock price hits its limits. A comparison is made of the properties between up-limit hits and down-limit hits, and the possible difference will also be compared between bullish and bearish market state by dividing the whole period into three alternating bullish periods and three bearish periods. We find that the cooling-off effect emerges for both up-limit hits and down-limit hits, and the cooling-off effect of the down-limit hits is stronger than that of the up-limit hits. The difference of the cooling-off effect between bullish period and bearish period is quite modest. Moreover, we examine the sub-optimal orders effect, and infer that the professional individual investors and institutional investors play a positive role in the cooling-off effects. All these findings indicate that the price limit trading rule exerts a positive effect on maintaining the stability of the Chinese stock markets.
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